Notre analyse va se porter sur 49 pays les plus atteint par le Covid-19 jusqu’au 28/04/2020, la base de données regroupe des informations sur le nombre de contamination / guéris / déces par le virus mais aussi des indicateurs comme GPP (global pandémic prepardness) ou le FPY ( Flights per year ) ..

Our analysis will be on the 49 countries most affected by the Coronavirus on thel ast count ‘28/04/2020’, we gathered information about confirmed cases, recovered cases, and deaths with some additional information about the countries.

2. Data structure :

str(df)

## 'data.frame':    49 obs. of  10 variables:
##  $ infected                          : int  6801 15597 9455 16705 49906 97100 56714 18435 82877 7285 ...
##  $ Population..millions.             : int  25448054 89977564 164403451 9449847 11580989 212298492 37684705 19087731 1438373881 50788168 ...
##  $ Density..Km.                      : int  3 109 1265 47 383 25 4 26 153 46 ...
##  $ median.age                        : num  37.9 43.5 27.6 40.3 41.9 33.5 41.1 35.3 38.4 31.3 ...
##  $ beds...1000                       : num  3.8 7.6 0.8 11 6.2 2.2 2.7 2.2 4.2 1.5 ...
##  $ GPP...global.pandemic.preparedness: num  75.5 58.5 35 35.3 61 59.7 75.3 58.3 48.2 44.2 ...
##  $ Income                            : Factor w/ 3 levels "high","lower/middle",..: 1 1 2 3 1 3 1 1 3 3 ...
##  $ FPY..flights.per.year             : int  665384 130260 101383 31676 140674 832683 1475063 134661 4692008 358847 ...
##  $ recovered                         : int  5814 13180 177 3117 12211 40937 23814 9572 78586 1666 ...
##  $ deaths                            : int  94 596 175 97 7765 6761 3684 247 4637 324 ...

3. Summary Stats :

##     infected       Population..millions.  Density..Km.    median.age   
##  Min.   :   6193   Min.   :2.872e+06     Min.   :   3   Min.   :22.80  
##  1st Qu.:   9523   1st Qu.:1.020e+07     1st Qu.:  49   1st Qu.:30.50  
##  Median :  18435   Median :3.768e+07     Median : 109   Median :38.30  
##  Mean   :  68960   Mean   :1.177e+08     Mean   : 332   Mean   :36.54  
##  3rd Qu.:  49906   3rd Qu.:8.998e+07     3rd Qu.: 225   3rd Qu.:42.20  
##  Max.   :1165868   Max.   :1.438e+09     Max.   :8358   Max.   :48.40  
##   beds...1000     GPP...global.pandemic.preparedness          Income  
##  Min.   : 0.600   Min.   :35.00                      high        :28  
##  1st Qu.: 1.600   1st Qu.:46.50                      lower/middle: 6  
##  Median : 2.800   Median :55.40                      upper/middle:15  
##  Mean   : 3.718   Mean   :55.11                                       
##  3rd Qu.: 4.700   3rd Qu.:62.20                                       
##  Max.   :13.400   Max.   :83.50                                       
##  FPY..flights.per.year   recovered          deaths     
##  Min.   :    1421      Min.   :    32   Min.   :   12  
##  1st Qu.:  119148      1st Qu.:  1534   1st Qu.:  229  
##  Median :  254064      Median :  4326   Median :  664  
##  Mean   :  716587      Mean   : 21082   Mean   : 4891  
##  3rd Qu.:  772926      3rd Qu.: 13386   3rd Qu.: 3336  
##  Max.   :11354693      Max.   :175382   Max.   :66369

a. Confirmed Cases :

b. Recovered cases :

c. Death cases :

a. Number of Confirmed cases per Income :

Number of Recovered cases per Income :

5. correlogram :

Calculate the PCA :

Extraction of eigenvalues / variances of the main components :

##       eigenvalue variance.percent cumulative.variance.percent
## Dim.1 3.78283850        42.031539                    42.03154
## Dim.2 1.87023532        20.780392                    62.81193
## Dim.3 1.06470437        11.830049                    74.64198
## Dim.4 0.97301185        10.811243                    85.45322
## Dim.5 0.65224698         7.247189                    92.70041
## Dim.6 0.35220916         3.913435                    96.61385
## Dim.7 0.17428476         1.936497                    98.55034
## Dim.8 0.11179442         1.242160                    99.79250
## Dim.9 0.01867464         0.207496                   100.00000

Visualize the eigenvalues. Shows the percentage of variances explained by each main axis:

Key Results: Cumulative, Eigenvalue, barplot In these results, the first four principal components have eigenvalues greater than 1. These three components explain 85.45% of the variation in the data. The barplot shows that the eigenvalues start to form a straight line after the fourth principal component. But to make sens or our results we will use only the first two components as they represent more then 60% of the variation in the data.

Description of dimensions:

## $quanti
##                                    correlation      p.value
## infected                             0.9455062 1.525080e-24
## deaths                               0.9230268 3.976206e-21
## FPY..flights.per.year                0.8813770 6.442516e-17
## recovered                            0.8503451 1.061037e-14
## GPP...global.pandemic.preparedness   0.5802849 1.240577e-05
## median.age                           0.3624675 1.048339e-02
## 
## $quali
##                 R2      p.value
## clusters 0.8368592 7.743584e-19
## 
## $category
##                       Estimate      p.value
## clusters=clusters_1  7.2162854 1.527916e-13
## ds=high              0.8859782 4.086720e-02
## clusters=clusters_2 -2.6437500 2.255358e-02
## clusters=clusters_3 -4.5725354 4.329677e-06
## 
## attr(,"class")
## [1] "condes" "list "

## $quanti
##                                    correlation      p.value
## median.age                           0.8617675 1.873946e-15
## beds...1000                          0.7746392 6.538558e-11
## GPP...global.pandemic.preparedness   0.4086202 3.557739e-03
## Population..millions.               -0.4962679 2.873127e-04
## 
## $quali
##           R2     p.value
## ds 0.2183344 0.003463241
## 
## $category
##                  Estimate     p.value
## ds=high          0.914282 0.001730232
## ds=lower/middle -0.844556 0.017074167
## 
## attr(,"class")
## [1] "condes" "list "

Graph of individuals. Coloring according to kmeans clustring by infected. Similar individuals are grouped together:

## Too few points to calculate an ellipse

As we can see in the graph above that US is concedered as an group by it self and the other two groups have some intersection and that’s probably because they have very close number of infected cases.

Graph of variables. Coloring according to the kmeans clustring of the variables. The positively correlated variables are on the same side of the graph. The negatively correlated variables are on opposite sides of the graph:

Here, we used kmeans segmentation to divide the variables and infact this graph confirme our interpretaion above that the infected cases, deaths recoveries and flight per year are highly correlated and this graph shows that they are in the same group of cluster which is very logic, the same goes for beds per 1000km², median age, and GPP. but we can see that it has grouped the density and population count which is very normal because the dansity is calculated based on the population count in the first place, but the cercle of corelation tells a diffirent story, these last two variables are negativily correlated plus the density per km² is badly represented here.

Coordinates of variables on main axes:

##                                          Dim.1       Dim.2       Dim.3
## infected                            0.94550621 -0.15270460  0.06201992
## Population..millions.               0.22784880 -0.49626791 -0.39805463
## Density..Km.                       -0.08330142  0.08300299  0.74719579
## median.age                          0.36246752  0.86176749 -0.04798405
## beds...1000                         0.09999117  0.77463924 -0.46194778
## GPP...global.pandemic.preparedness  0.58028489  0.40862020  0.32171733
## FPY..flights.per.year               0.88137704 -0.27118185 -0.05511578
## recovered                           0.85034508 -0.08794865 -0.09747378
## deaths                              0.92302684 -0.05283089  0.11121919
##                                          Dim.4       Dim.5
## infected                           -0.08358150 -0.19939353
## Population..millions.               0.63119902  0.36268821
## Density..Km.                        0.62758265 -0.17823251
## median.age                          0.19137179  0.10429020
## beds...1000                         0.24777144 -0.22882491
## GPP...global.pandemic.preparedness -0.19354036  0.57542262
## FPY..flights.per.year               0.12535300  0.02682055
## recovered                           0.03524162 -0.19743798
## deaths                             -0.14603677 -0.12300428

Cos2: quality of representation of the variables on the main axes:

##                                          Dim.1       Dim.2       Dim.3
## infected                           0.893982000 0.023318696 0.003846471
## Population..millions.              0.051915074 0.246281834 0.158447491
## Density..Km.                       0.006939126 0.006889496 0.558301550
## median.age                         0.131382705 0.742643211 0.002302469
## beds...1000                        0.009998235 0.600065955 0.213395748
## GPP...global.pandemic.preparedness 0.336730558 0.166970471 0.103502041
## FPY..flights.per.year              0.776825494 0.073539593 0.003037749
## recovered                          0.723086756 0.007734965 0.009501138
## deaths                             0.851978555 0.002791103 0.012369709
##                                          Dim.4        Dim.5
## infected                           0.006985866 0.0397577811
## Population..millions.              0.398412207 0.1315427406
## Density..Km.                       0.393859979 0.0317668275
## median.age                         0.036623161 0.0108764448
## beds...1000                        0.061390685 0.0523608389
## GPP...global.pandemic.preparedness 0.037457870 0.3311111941
## FPY..flights.per.year              0.015713375 0.0007193416
## recovered                          0.001241972 0.0389817574
## deaths                             0.021326737 0.0151300539

Contribution of variables to main axes:

##                                         Dim.1      Dim.2      Dim.3      Dim.4
## infected                           23.6325711  1.2468322  0.3612713  0.7179631
## Population..millions.               1.3723841 13.1684944 14.8818297 40.9462851
## Density..Km.                        0.1834370  0.3683759 52.4372368 40.4784359
## median.age                          3.4731249 39.7085437  0.2162543  3.7638967
## beds...1000                         0.2643051 32.0850509 20.0427231  6.3093461
## GPP...global.pandemic.preparedness  8.9015314  8.9277787  9.7212000  3.8496828
## FPY..flights.per.year              20.5355183  3.9321037  0.2853139  1.6149212
## recovered                          19.1149254  0.4135825  0.8923734  0.1276420
## deaths                             22.5222027  0.1492381  1.1617975  2.1918270
##                                         Dim.5
## infected                            6.0955102
## Population..millions.              20.1676274
## Density..Km.                        4.8703679
## median.age                          1.6675347
## beds...1000                         8.0277626
## GPP...global.pandemic.preparedness 50.7646956
## FPY..flights.per.year               0.1102867
## recovered                           5.9765332
## deaths                              2.3196817

INDIVIDUALS : quality and contribution:

Here we can remark that the most of the countries that have high quality of representation on the first component are mostly the medium and high income countries if we make couple steps behind to the 1st dim analysis we said that the infected variable is the most representative on it, plus we expressed it with the variable flights per year, here actually it makes lot of sens because normaly we you ( as a country ) have medium or high income means that you have medium or big aeroports and with you’ll have medium to high number of flights per year ! same goes for the 2nd dimenstion, the more income you have the more health care you will provide for your citizents.

just to verify our choice we will use the 26 creterias :

## *** : The Hubert index is a graphical method of determining the number of clusters.
##                 In the plot of Hubert index, we seek a significant knee that corresponds to a 
##                 significant increase of the value of the measure i.e the significant peak in Hubert
##                 index second differences plot. 
## 

## *** : The D index is a graphical method of determining the number of clusters. 
##                 In the plot of D index, we seek a significant knee (the significant peak in Dindex
##                 second differences plot) that corresponds to a significant increase of the value of
##                 the measure. 
##  
## ******************************************************************* 
## * Among all indices:                                                
## * 9 proposed 3 as the best number of clusters 
## * 5 proposed 4 as the best number of clusters 
## * 3 proposed 5 as the best number of clusters 
## * 1 proposed 7 as the best number of clusters 
## * 3 proposed 8 as the best number of clusters 
## * 3 proposed 9 as the best number of clusters 
## 
##                    ***** Conclusion *****                            
##  
## * According to the majority rule, the best number of clusters is  3 
##  
##  
## *******************************************************************

## Among all indices: 
## ===================
## * 2 proposed  0 as the best number of clusters
## * 9 proposed  3 as the best number of clusters
## * 5 proposed  4 as the best number of clusters
## * 3 proposed  5 as the best number of clusters
## * 1 proposed  7 as the best number of clusters
## * 3 proposed  8 as the best number of clusters
## * 3 proposed  9 as the best number of clusters
## 
## Conclusion
## =========================
## * According to the majority rule, the best number of clusters is  3 .

so this histograme above shows us that the majority of creterias has proposed 3 clusters

the dendrogram:

this dendrogram above tells the same story as the results from the clValid package, and the PCA individuals plot clustred by kmeans. three major clusters are present here, if we make the relation between the classification results and the PCA results we can say that the blue cluster (right group) are the medium to low and low incom countries, as result these countries have the lowest infected cases recorded and that’s because as we said before they dont have a high number of flights, and the green cluster (middle group) are the medium to high and high incom countries respectively medium to high and high number of flights per year, the last cluster the red cluster it is an individual by it’s self and that’s normal because US have the highest number of flights per year and now it’s recording the highest number of infected cases and it represent by it’s self 50% of the infected cases!

SUM-up interpretations:

the number 1 factor in the evolution of infected cases is the flights per year indicator!

proof : USA has the highest number of Flights per year and the Highest number of infected cases

the GPP, global pandemic preparedness indicator does not explain the percentage of the recoveries.

the general health idicators (see in PCA results), did not explain if a country could be effective against the virus or not !

the numbers of deaths increases where a country have a median age above 41.